Problem: Solve for $x$ and $y$ using elimination. ${2x+y = 14}$ ${5x+4y = 38}$
Solution: We can eliminate $y$ by adding the equations together when the $y$ coefficients have opposite signs. Multiply the top equation by $-4$ ${-8x-4y = -56}$ $5x+4y = 38$ Add the top and bottom equations together. $-3x = -18$ $\dfrac{-3x}{{-3}} = \dfrac{-18}{{-3}}$ ${x = 6}$ Now that you know ${x = 6}$ , plug it back into $\thinspace {2x+y = 14}\thinspace$ to find $y$ ${2}{(6)}{ + y = 14}$ $12+y = 14$ $12{-12} + y = 14{-12}$ ${y = 2}$ You can also plug ${x = 6}$ into $\thinspace {5x+4y = 38}\thinspace$ and get the same answer for $y$ : ${5}{(6)}{ + 4y = 38}$ ${y = 2}$